If an electrostatic field exists in space around stationary electric charges, then in space around moving charges (as well as around time-varying electric fields, which Maxwell originally suggested) exists. This is easy to observe experimentally.
It is thanks to the magnetic field that electric currents interact with each other, as well as permanent magnets and currents with magnets. Compared to the electrical interaction, the magnetic interaction is much stronger. This interaction was studied in due time by André-Marie Ampere.
In physics, the characteristic of the magnetic field is B, and the larger it is, the stronger the magnetic field. Magnetic induction B is a vector quantity, its direction coincides with the direction of the force acting on the north pole of a conventional magnetic arrow placed at some point of the magnetic field - the magnetic field will orient the magnetic arrow in the direction of vector B, that is, in the direction of the magnetic field.
Vector B at each point of the magnetic induction line is directed to it tangentially. That is, induction B characterizes the force effect of the magnetic field on the current. A similar role is played by the strength E for the electric field, which characterizes the forceful action of the electric field on the charge.
The simplest experiment with iron filings allows you to clearly demonstrate the phenomenon of the action of a magnetic field on a magnetized object, since in a constant magnetic field, small pieces of a ferromagnet (such pieces are iron filings) become, magnetized along the field, magnetic arrows, like small arrows of a compass.
If you take a vertical copper conductor, and pass it through a hole in a horizontally located sheet of paper (or plexiglass, or plywood), and then pour metal filings on the sheet, shake it a little, and then pass a direct current through the conductor, it is easy to see how the sawdust will line up in the form of a vortex in circles around the conductor, in a plane perpendicular to the current in it.
These sawdust circles will just be a conventional image of the lines of magnetic induction B of the magnetic field of a conductor with current. The center of the circles, in this experiment, will be located exactly in the center, along the axis of the conductor with current.
The direction of the vectors of magnetic induction In a conductor with a current can be easily determined either according to the rule of the right screw: when the screw axis translates in the direction of the current in the conductor, the direction of rotation of the screw or gimbal handle (screw in or out) will indicate the direction of the magnetic field around the current.
Why does the gimbal rule apply? Since the rotor operation (denoted in field theory by rot), used in two Maxwell equations, can be written formally as a vector product (with the nabla operator), and most importantly because the rotor of a vector field can be likened (is an analogy) to the angular velocity of rotation of the ideal liquid (as Maxwell himself imagined), the flow velocity field of which represents a given vector field, can be used for the rotor by those formulations of the rule that are described for the angular velocity.
Thus, if you twist the thumb in the direction of the vortex of the vector field, then it will be screwed in the direction of the vector of the rotor of this field.
As you can see, unlike the lines of intensity of the electrostatic field, which are open in space, the lines of magnetic induction surrounding the electric current are closed. If the lines of electrical intensity E begin at positive charges and end at negative charges, then the lines of magnetic induction B are simply closed around the current that generates them.
Now let's complicate the experiment. Consider, instead of a straight conductor with current, a turn with current. Suppose it is convenient for us to position such a contour perpendicular to the plane of the drawing, with the current directed to us on the left, and on the right from us. If now a compass with a magnetic arrow is placed inside the loop with current, then the magnetic arrow will indicate the direction of the lines of magnetic induction - they will be directed along the axis of the loop.
Why? Because the opposite sides of the plane of the coil will be analogous to the poles of the magnetic needle. From where the B lines go out is the north magnetic pole, where they come in - the south pole. This is easy to understand if you first consider a conductor with current and its magnetic field, and then simply roll the conductor into a ring.
To determine the direction of the magnetic induction of a loop with a current, they also use the gimbal rule or the right screw rule. Place the gimbal tip in the center of the loop and rotate it clockwise. The translational movement of the gimbal will coincide in direction with the vector of magnetic induction B in the center of the loop.
Obviously, the direction of the magnetic field of the current is related to the direction of the current in the conductor, be it a straight conductor or a coil.
It is generally accepted that the side of the coil or coil with current from where the lines of magnetic induction B go out (the direction of vector B is outward) is the north magnetic pole, and where the lines enter (vector B is directed inward) is the south magnetic pole.
If many turns with current form a long coil - a solenoid (the length of the coil is many times its diameter), then the magnetic field inside it is uniform, that is, the lines of magnetic induction B are parallel to each other, and have the same density along the entire length of the coil. By the way, the magnetic field of a permanent magnet is similar from the outside to the magnetic field of a coil with current.
For a coil with a current I, length l, with the number of turns N, the magnetic induction in vacuum will be numerically equal to:
So, the magnetic field inside the coil with current is uniform, and is directed from the south to the north pole (inside the coil!). The magnetic induction inside the coil is proportional in modulus to the number of ampere-turns per unit length of the coil with current.
What do you mean by the word "coil"? Well ... this is probably some kind of "fig" on which threads, fishing line, rope, whatever! An inductor is exactly the same thing, but instead of a thread, fishing line or anything else, ordinary copper wire is wound there in isolation.
Insulation can be of colorless varnish, PVC insulation and even cloth. Here the trick is such that although the wires in the inductor are very tightly adjacent to each other, they still isolated from each other... If you wind the inductors with your own hands, in no case do not try to take an ordinary bare copper wire!
Inductance
Any inductor has inductance... Coil inductance is measured in Henry(Gn), denoted by a letter L and measured with an LC meter.
What is inductance? If an electric current is passed through the wire, then it will create a magnetic field around itself:
where
B - magnetic field, Wb
I -
Let's take and wind this wire into a spiral and apply voltage to its ends
And we get this picture with magnetic lines of force:
Roughly speaking, the more magnetic field lines cross the area of this solenoid, in our case the area of the cylinder, the greater the magnetic flux (F)... Since an electric current flows through the coil, it means that a current with a current strength passes through it (I), and the coefficient between magnetic flux and current is called inductance and is calculated by the formula:
From a scientific point of view, inductance is the ability to extract energy from an electric current source and store it in the form of a magnetic field. If the current in the coil increases, the magnetic field around the coil expands, and if the current decreases, then the magnetic field contracts.
Self-induction
The inductor also has a very interesting property. When a constant voltage is applied to the coil, an opposite voltage is generated in the coil for a short period of time.
This opposite tension is called EMF of self-induction. This depends on the value of the inductance of the coil. Therefore, at the moment the voltage is applied to the coil, the current gradually changes its value from 0 to a certain value within fractions of a second, because the voltage, at the moment of supplying an electric current, also changes its value from zero to a steady value. According to Ohm's Law:
where
I- current strength in the coil, A
U- coil voltage, V
R- coil resistance, Ohm
As we can see from the formula, the voltage changes from zero to the voltage supplied to the coil, therefore, the current will also change from zero to some value. The coil resistance for direct current is also constant.
And the second phenomenon in the inductor coil is that if we open the circuit of the inductor coil - the current source, then our EMF of self-induction will add up to the voltage that we have already applied to the coil.
That is, as soon as we break the circuit, the voltage on the coil at this moment can be several times higher than it was before the circuit was opened, and the current in the coil circuit will quietly drop, since the EMF of self-induction will support the decreasing voltage.
Let's make the first conclusions about the operation of the inductor when DC is applied to it. When an electric current is applied to the coil, the current will gradually increase, and when the electric current is removed from the coil, the current will gradually decrease to zero. In short, the current in the coil cannot change instantly.
Types of inductors
Inductors are mainly divided into two classes: with magnetic and non-magnetic core... Below in the photo is a coil with a non-magnetic core.
But where is her core? Air is a non-magnetic core :-). Such coils can also be wound on a cylindrical paper tube. The inductance of non-magnetic core coils is used when the inductance does not exceed 5 millihenry.
And here are the core inductors:
Ferrite and iron plate cores are mainly used. Cores increase the inductance of the coils at times. Ring-shaped cores (toroidal) allow for higher inductance than just cores from a cylinder.
For medium inductors, ferrite cores are used:
High inductance coils are made like a transformer with an iron core, but with one winding, unlike a transformer.
Chokes
There is also a special kind of inductor. This is the so-called. An inductor is an inductor whose job it is to create a large AC resistance in the circuit in order to suppress high frequency currents.
Direct current flows through the inductor without any problem. You can read why this happens in this article. Typically, chokes are included in the power supply circuits of amplifying devices. Chokes are designed to protect power supplies from the ingress of high-frequency signals (HF signals). At low frequencies (LF) they are used by power circuits and usually have metal or ferrite cores. Below in the photo are power chokes:
There is also another special type of chokes - this. It consists of two oppositely wound inductors. Due to counter winding and mutual induction, it is more efficient. Dual chokes are widely used as input filters for power supplies, as well as in audio technology.
Coil experiments
What factors does the inductance of a coil depend on? Let's do some experiments. I wound a coil with a non-magnetic core. Its inductance is so small that the LC meter shows zero to me.
Ferrite core available
I start to insert the coil into the core to the very edge
The LC meter shows 21 microhenries.
I put the coil in the middle of the ferrite
35 microhenry. Better now.
I continue to insert the coil on the right edge of the ferrite
20 microhenry. We conclude the largest inductance on a cylindrical ferrite occurs in its middle. Therefore, if you wind on a cylinder, try to wind in the middle of the ferrite. This property is used to smoothly change inductance in variable inductors:
where
1 is the coil frame
2 is the turns of the coil
3 - a core with a groove on top for a small screwdriver. By twisting or unscrewing the core, we thereby change the inductance of the coil.
The inductance is almost 50 microhenry!
Let's try to straighten the turns throughout the ferrite
13 microhenry. We conclude: for maximum inductance, wind the coil “turn to turn”.
Let's reduce the turns of the coil by half. There were 24 turns, now it is 12.
Very little inductance. I reduced the number of turns by 2 times, the inductance decreased by 10 times. Conclusion: the fewer the number of turns, the lower the inductance and vice versa. The inductance does not change in a straight line to the turns.
Let's experiment with a ferrite bead.
Measuring inductance
15 microhenry
Let's remove the turns of the coil from each other
We measure again
Hmm, also 15 microhenry. We conclude: the distance from turn to turn does not play any role in the toroidal inductor.
We wind more turns. There were 3 turns, now it is 9.
We measure
Fuck! I increased the number of turns by 3 times, and the inductance increased by 12 times! Output: the inductance does not change in a straight line to the turns.
If you believe the formulas for calculating inductances, inductance depends on "turns squared". I will not lay out these formulas here, because I do not see the need. I will only say that the inductance also depends on such parameters as the core (what material it is made of), the cross-sectional area of the core, and the length of the coil.
Designation on the diagrams
Series and parallel connection of coils
At series connection of inductors, their total inductance will be equal to the sum of the inductances.
And when parallel connection we get like this:
When connecting inductors, the as a rule, they should be spatially separated on the board. This is due to the fact that when they are close to each other, their magnetic fields will influence each other, and therefore the inductance readings will be incorrect. Do not place two or more toroidal coils on one iron axle. This can lead to incorrect total inductance readings.
Summary
The inductor plays a very important role in electronics, especially in transceiver equipment. Various inductors are also built on inductors for electronic radio equipment, and in electrical engineering it is also used as a current surge limiter.
The guys from the Soldering Iron made a very good video about the inductor. I advise you to look without fail:
The conductor through which the electric current flows creates a magnetic field which is characterized by the intensity vector `H(fig. 3). The magnetic field strength obeys the principle of superposition
a, according to the Bio-Savart-Laplace law,
where I- current in a conductor, - a vector having the length of an elementary segment of a conductor and directed in the direction of the current, `r- radius vector connecting the element with the point in question P.
One of the most common configurations of conductors with current is a loop in the form of a ring of radius R (Fig. 3, a). The magnetic field of such a current in the plane passing through the axis of symmetry has the form (see Fig. 3, b). The field as a whole should have rotational symmetry about the z-axis (Fig. 3, b), and the lines of force themselves should be symmetrical about the plane of the loop (plane xy). The field in the immediate vicinity of the conductor will resemble the field in the vicinity of a long straight wire, since here the influence of the distant parts of the loop is relatively small. On the axis of the circular current, the field is directed along the axis Z.
Let's calculate the strength of the magnetic field on the axis of the ring at a point located at a distance z from the plane of the ring. By formula (6), it is enough to calculate the z-component of the vector:
. (7)
Integrating over the entire ring, we get òd l= 2p R... Since, according to the Pythagorean theorem r 2 = R 2 + z 2, then the required field at a point on the axis is equal in magnitude to
. (8)
Vector direction `H can be directed according to the rule of the right screw.
In the center of the ring z= 0 and formula (8) is simplified:
We are interested in short coil- a cylindrical wire reel consisting of N turns of the same radius. Due to axial symmetry and in accordance with the principle of superposition, the magnetic field of such a coil on the H axis is the algebraic sum of the fields of the individual turns H i:. Thus, the magnetic field of a short coil containing N to turns, at an arbitrary point on the axis is calculated by the formulas
, 
, (10)
where H- tension, B- magnetic field induction.
Solenoid magnetic field with current
To calculate the induction of the magnetic field in the solenoid, the theorem on the circulation of the magnetic induction vector is used:
, (11)
where is the algebraic sum of the currents covered by the circuit L free form, n- the number of conductors with currents covered by the circuit. In this case, each current is taken into account as many times as it is covered by the contour, and the current is considered positive, the direction of which forms a right-handed screw system with the direction of bypassing along the contour, - an element of the contour L.
We apply the theorem on the circulation of the magnetic induction vector to a solenoid of length l having N from loops with amperage I(fig. 4). In the calculation, we will take into account that almost the entire field is concentrated inside the solenoid (we neglect the edge effects) and it is homogeneous. Then formula 11 will take the form:
,
whence we find the induction of the magnetic field created by the current inside the solenoid:
 |
Rice. 4. Solenoid with current and its magnetic field
Installation diagram
Rice. 5 Schematic electrical diagram of the installation
1 - magnetic field induction meter (teslameter), A - ammeter, 2 - connecting wire, 3 - measuring probe, 4 - Hall sensor *, 5 - object under study (short coil, straight conductor, solenoid), 6 - current source, 7 - a ruler for fixing the position of the sensor, 8 - stylus holder.
* - the principle of operation of the sensor is based on the phenomenon of the Hall effect (see lab. Work No. 15 Study of the Hall effect)
Work order
1. Study of the magnetic field of a short coil
1.1. Switch on the devices. The power supply and teslameter switches are located on the rear panels.
1.2. Install a short coil in the holder as a test object 5 (see Fig. 5) and connect it to a current source 6.
1.3. Set the voltage regulator at source 6 to the middle position. Set the current strength to zero by adjusting the current output at the source 6 and check with an ammeter (the value should be zero).
1.4. Adjust the coarse 1 and fine adjustment knobs 2 (Fig. 6) to achieve zero teslameter readings.
1.5. Place the holder with the measuring probe on the ruler in a position that is convenient for reading - for example, at the coordinate of 300 mm. In the future, take this provision as zero. During installation and during measurements, observe the parallelism between the stylus and the ruler.
1.6. Position the holder with the short coil so that the Hall sensor 4 is in the center of the coil turns (fig. 7). To do this, use the height clamping screw on the dipstick holder. The plane of the coil must be perpendicular to the stylus. In the process of preparing measurements, move the holder with the test sample, leaving the measuring probe motionless.
1.7. Make sure that during the warming up of the teslameter, its readings remain zero. If this is not done, set the teslameter to zero at zero current in the sample.
1.8. Set the current in the short coil to 5 A (by adjusting the output on power supply 6, Constanter / Netzgerät Universal).
1.9. Measure magnetic induction B exp on the axis of the coil depending on the distance to the center of the coil. To do this, move the stylus holder along a straight edge, keeping it parallel to its original position. Negative z values correspond to the stylus displacement to an area of smaller coordinates than the initial one, and vice versa - positive z values - to the area of larger coordinates. Enter the data in table 1.
Table 1 Dependence of the magnetic induction on the axis of a short coil on the distance to the center of the coil
1.10. Repeat steps 1.2 - 1.7.
1.11. Measure the dependence of the induction in the center of the loop on the current passing through the coil. Enter the data in table 2.
Table 2 Dependence of the magnetic induction in the center of a short coil on the current in it
2. Study of the magnetic field of the solenoid
2.1. Install the solenoid on a height-adjustable metal bench made of non-magnetic material as a test object 5 (Fig. 8).
2.2. Repeat 1.3 - 1.5.
2.3. Adjust the height of the bench so that the dipstick runs along the axis of symmetry of the solenoid and the Hall sensor is in the middle of the turns of the solenoid.
2.4. Repeat steps 1.7 - 1.11 (instead of a short coil, a solenoid is used here). Enter the data into tables 3 and 4, respectively. In this case, determine the coordinate of the center of the solenoid as follows: install the Hall sensor at the beginning of the solenoid and fix the coordinate of the holder. Then move the holder along the ruler along the solenoid axis until the end of the sensor is on the other side of the solenoid. Fix the coordinate of the holder in this position. The solenoid center coordinate will be equal to the arithmetic mean of the two measured coordinates.
Table 3 Dependence of the magnetic induction on the axis of the solenoid from the distance to its center.
2.5. Repeat steps 1.3 - 1.7.
2.6. Measure the dependence of the induction in the center of the solenoid on the current flowing through the coil. Enter the data in table 4.
Table 4 Dependence of the magnetic induction in the center of the solenoid on the current in it
3. Study of the magnetic field of a straight conductor with current
3.1. Install a straight conductor with current as the object under study (Fig. 9, a). To do this, connect the wires from the ammeter and the power source to each other (short-circuit the external circuit) and place the conductor directly on the edge of probe 3 at probe 4, perpendicular to the probe (Fig. 9, b). To support the conductor, use a height-adjustable metal bench made of non-magnetic material on one side of the probe and a holder for the test samples on the other side (you can plug the conductor clamp into one of the holder slots for more reliable fixation of this conductor). Give the conductor a straight line.
3.2. Repeat steps 1.3 - 1.5.
3.3. Determine the dependence of the magnetic induction on the current in the conductor. Enter the measured data in table 5.
Table 5 Dependence of the magnetic induction created by a straight conductor on the current in it
4. Determination of the parameters of the investigated objects
4.1. Determine (if necessary, measure) and record in Table 6 the data necessary for calculations: N to- the number of turns of the short coil, R- its radius; N with- the number of turns of the solenoid, l- its length, L- its inductance (indicated on the solenoid), d Is its diameter.
Table 6 Parameters of the studied samples
| N To | R | N with | d | l | L |
Processing of results
1. Using the formula (10), calculate the magnetic induction created by a short coil with current. Enter the data in tables 1 and 2. According to table 1, construct the theoretical and experimental dependence of the magnetic induction on the axis of the short coil from the distance z to the center of the coil. Construct theoretical and experimental dependences in the same coordinate axes.
2. According to table 2, construct the theoretical and experimental dependence of the magnetic induction in the center of a short coil on the current in it. Construct theoretical and experimental dependences in the same coordinate axes. Calculate the magnetic field strength in the center of the coil with a current strength of 5 A in it using formula (10).
3. Using the formula (12), calculate the magnetic induction created by the solenoid. Enter the data in tables 3 and 4. According to table 3, construct the theoretical and experimental dependence of the magnetic induction on the axis of the solenoid from the distance z to its center. Construct theoretical and experimental dependences in the same coordinate axes.
4. According to table 4, construct the theoretical and experimental dependence of the magnetic induction in the center of the solenoid on the current in it. Construct theoretical and experimental dependences in the same coordinate axes. Calculate the strength of the magnetic field in the center of the solenoid with a current strength of 5 A.
5. According to table 5, construct the experimental dependence of the magnetic induction created by the conductor on the current in it.
6. Based on formula (5), determine the shortest distance r o from the sensor to the conductor with current (this distance is determined by the thickness of the conductor insulation and the thickness of the sensor insulation in the probe). Enter the calculation results in table 5. Calculate the arithmetic mean r o, compare with the visually observed value.
7. Calculate the inductance of the solenoid L. Enter the calculation results in table 4. Compare the obtained average value L with the fixed value of inductance in table 6. To calculate, use the formula, where Y- flux linkage, Y = N with BS, where V- magnetic induction in the solenoid (according to table 4), S= p d 2/4 - solenoid cross-sectional area.
Control questions
1. What is the Bio-Savart-Laplace law and how can it be applied when calculating the magnetic fields of current-carrying conductors?
2. How the direction of the vector is determined H in the Bio-Savart-Laplace law?
3. How are the vectors of magnetic induction interconnected B and tensions H between themselves? What are their units of measurement?
4. How is Bio-Savart-Laplace's law used in calculating magnetic fields?
5. How is the magnetic field measured in this work? What physical phenomenon is the principle of magnetic field measurement based on?
6. Give the definition of inductance, magnetic flux, flux linkage. Specify the units for these quantities.
bibliographic list
educational literature
1. Kalashnikov N.P. Fundamentals of Physics. M .: Bustard, 2004.Vol. 1
2. Saveliev I.V... Physics course. Moscow: Nauka, 1998.Vol. 2.
3. Detlaf A.A.,Yavorskiy B.M. Physics course. M .: Higher school, 2000.
4. Irodov I.E Electromagnetism. M .: Binom, 2006.
5. Yavorskiy B.M.,Detlaf A.A. Physics Handbook. Moscow: Nauka, 1998.
Greetings to everyone on our website!
We continue to study electronics from the very beginning, that is, from the very foundations and the topic of today's article will be principle of operation and basic characteristics of inductors... Looking ahead, I will say that first we will discuss the theoretical aspects, and several future articles will devote entirely and completely to the consideration of various electrical circuits in which inductors are used, as well as the elements that we studied earlier in our course - and.
The device and principle of operation of the inductor.
As it is already clear from the name of the element, an inductance coil, first of all, is just a coil :), that is, a large number of turns of an insulated conductor. Moreover, the presence of insulation is the most important condition - the coil turns should not close with each other. Most often, the turns are wound on a cylindrical or toroidal frame:
The most important characteristic inductors is, of course, inductance, otherwise why would it be given such a name 🙂 Inductance is the ability to convert the energy of an electric field into the energy of a magnetic field. This property of the coil is due to the fact that when a current flows through a conductor, a magnetic field arises around it:
And here is what the magnetic field looks like when current passes through the coil:
In general, strictly speaking, any element in an electrical circuit has inductance, even an ordinary piece of wire. But the fact is that the value of such an inductance is very insignificant, in contrast to the inductance of coils. Actually, in order to characterize this value, the Henry unit (Hn) is used. 1 Henry is actually a very large value, so μH (microhenry) and mH (millhenry) are most often used. The value inductance coils can be calculated using the following formula:
Let's see what kind of value is included in this expression:
It follows from the formula that with an increase in the number of turns or, for example, the diameter (and, accordingly, the cross-sectional area) of the coil, the inductance will increase. And with an increase in length - to decrease. Thus, the turns on the coil should be placed as close to each other as possible, as this will reduce the length of the coil.
WITH coil device we figured it out, it's time to consider the physical processes that occur in this element when an electric current passes. To do this, we will consider two schemes - in one we will pass a direct current through the coil, and in the other, an alternating current 🙂
So, first of all, let's figure out what happens in the coil itself when current flows. If the current does not change its magnitude, then the coil has no effect on it. Does this mean that in the case of direct current, the use of inductors is not worth considering? But no 🙂 After all, direct current can be turned on / off, and just at the moments of switching, all the most interesting happens. Let's take a look at the chain:
In this case, the resistor plays the role of a load, in its place could be, for example, a lamp. In addition to the resistor and inductance, a constant current source and a switch are included in the circuit, with which we will close and open the circuit.
What happens the moment we close the switch?
Coil current will begin to change, since at the previous moment in time it was equal to 0. A change in current will lead to a change in the magnetic flux inside the coil, which, in turn, will cause the emergence of EMF (electromotive force) of self-induction, which can be expressed as follows:
The emergence of an EMF will lead to the appearance of an induction current in the coil, which will flow in the opposite direction to the direction of the power supply current. Thus, the EMF of self-induction will prevent the flow of current through the coil (the induction current will compensate for the circuit current due to the fact that their directions are opposite). This means that at the initial moment of time (immediately after the switch is closed) the current through the coil will be equal to 0. At this moment in time, the EMF of self-induction is maximum. What happens next? Since the magnitude of the EMF is directly proportional to the rate of change of the current, it will gradually weaken, and the current, respectively, on the contrary, will increase. Let's take a look at some graphs that illustrate what we've discussed:
In the first chart, we see circuit input voltage- initially the circuit is open, and when the switch closes, a constant value appears. In the second chart, we see change in the magnitude of the current through the coil inductance. Immediately after the key is closed, there is no current due to the occurrence of EMF of self-induction, and then it begins to increase smoothly. On the contrary, the voltage on the coil is maximum at the initial moment of time, and then decreases. The graph of the voltage across the load will in shape (but not in magnitude) coincide with the graph of the current through the coil (since with a series connection, the current flowing through different elements of the circuit is the same). Thus, if we use a lamp as a load, then they will not light up immediately after the switch is closed, but with a slight delay (in accordance with the current graph).
A similar transient process in the circuit will be observed when the key is opened. An EMF of self-induction will appear in the inductor, but in the event of an opening, the inductive current will be directed in the same direction as the current in the circuit, and not in the opposite direction, therefore, the stored energy of the inductor will go to maintain the current in the circuit:
After the key is opened, an EMF of self-induction arises, which prevents the current through the coil from decreasing, so the current does not reach zero immediately, but after some time. The voltage in the coil is identical in shape to the closure of the switch, but opposite in sign. This is due to the fact that the change in the current, and, accordingly, the EMF of self-induction in the first and second cases are opposite in sign (in the first case, the current increases, and in the second, decreases).
By the way, I mentioned that the value of the EMF of self-induction is directly proportional to the rate of change of the current strength, and so, the coefficient of proportionality is nothing more than the inductance of the coil:
This is where we end up with inductors in DC circuits and move on to AC circuits.
Consider a circuit in which an alternating current is applied to the inductor:
Let's look at the dependences of the current and EMF of self-induction on time, and then we'll figure out why they look exactly like this:
As we have already found out EMF of self-induction we have it is directly proportional and opposite in sign to the rate of change of the current:
Actually, the graph demonstrates this dependence to us 🙂 See for yourself - between points 1 and 2 the current changes, and the closer to point 2, the less changes, and at point 2 the current does not change at all for a short period of time its meaning. Accordingly, the rate of change of the current is maximum at point 1 and smoothly decreases when approaching point 2, and at point 2 it is equal to 0, which we see on self-induction EMF graph... Moreover, over the entire interval 1-2, the current increases, which means that the rate of its change is positive, in this regard, on the EMF throughout this interval, on the contrary, takes negative values.
Similarly, between points 2 and 3 - the current decreases - the rate of change of the current is negative and increases - the EMF of self-induction increases and is positive. I will not describe the rest of the schedule - all processes there follow the same principle 🙂
In addition, a very important point can be noticed on the graph - when the current increases (sections 1-2 and 3-4), the self-induction EMF and current have different signs (section 1-2:, title = "(! LANG: Rendered by QuickLaTeX.com" height="12" width="39" style="vertical-align: 0px;">, участок 3-4: title="Rendered by QuickLaTeX.com" height="12" width="41" style="vertical-align: 0px;">, ). Таким образом, ЭДС самоиндукции препятствует возрастанию тока (индукционные токи направлены “навстречу” току источника). А на участках 2-3 и 4-5 все наоборот – ток убывает, а ЭДС препятствует убыванию тока (поскольку индукционные токи будут направлены в ту же сторону, что и ток источника и будут частично компенсировать уменьшение тока). И в итоге мы приходим к очень интересному факту – катушка индуктивности оказывает сопротивление переменному току, протекающему по цепи. А значит она имеет сопротивление, которое называется индуктивным или реактивным и вычисляется следующим образом:!}
Where is the circular frequency:. - this is .
Thus, the higher the frequency of the current, the greater the resistance the inductor will have. And if the current is constant (= 0), then the reactance of the coil is 0, respectively, it does not affect the flowing current.
Let's go back to our graphs, which we built for the case of using an inductor in an AC circuit. We have determined the EMF of the self-induction of the coil, but what will be the voltage? Everything is really simple here 🙂 According to the 2nd Kirchhoff's law:
And consequently:
Let's build on one graph the dependence of the current and voltage in the circuit on time:
As you can see, the current and voltage are phase-shifted () relative to each other, and this is one of the most important properties of AC circuits that use an inductor:
When the inductor is connected to an alternating current circuit, a phase shift appears in the circuit between voltage and current, while the current lags in phase from the voltage by a quarter of a period.
So we figured out the inclusion of the coil in the AC circuit 🙂
On this, perhaps, we will finish today's article, it has already turned out to be quite voluminous, so we will continue to talk about inductors next time. So see you soon, we will be glad to see you on our website!
If a straight conductor is rolled in the form of a circle, then the magnetic field of the circular current can be investigated.
Let's carry out experiment (1). We pass the wire in the form of a circle through the cardboard. Place some free magnetic arrows on the surface of the cardboard at different points. Turn on the current and see that the magnetic arrows in the center of the loop show the same direction, and outside the loop on both sides in the other direction.
Now we repeat experiment (2), changing the poles, and hence the direction of the current. We see that the magnetic arrows have changed direction on the entire surface of the cardboard by 180 degrees.
Let's conclude: the magnetic lines of circular current also depend on the direction of the current in the conductor.
Let's carry out experiment 3. Remove the magnetic arrows, turn on the electric current and carefully pour small iron filings over the entire surface of the cardboard. We have a picture of magnetic lines of force, which is called the "spectrum of the magnetic field of circular current." How, in this case, to determine the direction of the magnetic lines of force? We apply the gimbal rule again, but applied to circular current. If the direction of rotation of the gimbal handle is combined with the direction of the current in the circular conductor, then the direction of translational movement of the gimbal will coincide with the direction of the magnetic field lines.
Let's consider several cases.
1. The plane of the coil lies in the plane of the sheet, the current flows along the coil clockwise. Rotating the loop clockwise, we determine that the magnetic lines of force in the center of the loop are directed inward of the loop "away from us". This is conventionally indicated by the "+" (plus) sign. Those. in the center of the loop we put "+"
2. The plane of the turn lies in the plane of the sheet, the current along the turn goes counterclockwise. Rotating the loop counterclockwise, we determine that the magnetic lines of force go out from the center of the loop "towards us". This is conventionally designated "∙" (dot). Those. at the center of the loop, we must put a dot ("∙").
If you wind a straight conductor around a cylinder, you get a coil with a current, or a solenoid.
Let us carry out experiment (4.) We use the same circuit for the experiment, only the wire is now passed through the cardboard in the form of a coil. Place several free magnetic arrows on the plane of the cardboard at different points: at both ends of the coil, inside the coil and on both sides outside. Let the coil be horizontal (left-to-right direction). Turn on the circuit and find that the magnetic arrows located along the axis of the coil point in one direction. We note that at the right end of the coil, the arrow shows that the lines of force enter the coil, which means it is the "south pole" (S), and in the left, the magnetic arrow shows that they are coming out, this is the "north pole" (N). On the outside of the coil, the magnetic arrows point in the opposite direction to the direction on the inside of the coil.
Let's carry out experiment (5). In the same circuit, we change the direction of the current. We will find that the direction of all the magnetic arrows has changed, they have rotated 180 degrees. We draw a conclusion: the direction of the magnetic lines of force depends on the direction of the current along the turns of the coil.
Let's carry out experiment (6). Let's remove the magnetic arrows and turn on the circuit. Carefully "salt with iron filings" the cardboard inside and outside the spool. Let's get a picture of the magnetic field lines, which is called the "spectrum of the magnetic field of the coil with current"
But how to determine the direction of the magnetic lines of force? The direction of the magnetic field lines is determined according to the gimbal rule in the same way as for a loop with a current: If the direction of rotation of the gimbal handle is combined with the direction of the current in the loops, then the direction of translational motion will coincide with the direction of the magnetic field lines inside the solenoid. The magnetic field of a solenoid is similar to the magnetic field of a permanent strip magnet. The end of the coil, from which the lines of force go out, will be the "north pole" (N), and the one into which the lines of force enter will be the "south pole" (S).
After the discovery of Hans Oersted, many scientists began to repeat his experiments, inventing new ones, in order to discover evidence of the connection between electricity and magnetism. The French scientist Dominique Arago placed an iron rod in a glass tube and wound a copper wire over it, through which an electric current was passed. As soon as Arago closed the electrical circuit, the iron rod became so highly magnetized that it pulled the iron keys towards it. It took considerable effort to rip off the keys. When Arago turned off the power supply, the keys fell off by themselves! So Arago invented the first electromagnet. Modern electromagnets consist of three parts: a winding, a core and an armature. The wires are placed in a special sheath that acts as an insulator. A multilayer coil is wound with a wire - an electromagnet winding. A steel bar is used as the core. The plate that is attracted to the core is called an anchor. Electromagnets are widely used in industry due to their properties: they quickly demagnetize when the current is turned off; they can be made in a variety of sizes, depending on the purpose; by changing the strength of the current, the magnetic action of the electromagnet can be regulated. Electromagnets are used in factories to carry steel and cast iron products. These magnets have great lifting power. Electromagnets are also used in electric bells, electromagnetic separators, microphones, and telephones. Today we examined the magnetic field of a circular current, a coil with a current. We got acquainted with electromagnets, their application in industry and in the national economy.
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